"Can you prove them" Proof PPT courseware 3

Description

"Can you prove them" Proof PPT courseware 3

Judgment axiom: Two triangles with three equal sides are congruent (SSS).

Two triangles are congruent (SAS) if their two sides and their angles are equal.

Two triangles are congruent (ASA) if the two angles and their included sides are equal.

Can you prove the following corollary using the above axioms?

Corollary: Two triangles are congruent (AAS) if the angles and the corresponding sides of one of the angles are equal.

Corollary: The bisector of the vertex of an isosceles triangle, the midline on the base, and the altitude on the base coincide with each other (three lines merge into one).

∵AB=AC, ∠1=∠2 (known).

∴BD=CD,AD⊥BC (the three lines of an isosceles triangle merge into one).

∵AB=AC, BD=CD (known).

∴∠1=∠2,AD⊥BC (the three lines of the isosceles triangle merge into one)

∵AB=AC, AD⊥BC (known).

∴BD=CD, ∠1=∠2 (three lines of an isosceles triangle merge into one)

The rotation conditions ∠1=∠2, AD⊥BC, BD=CD can be used in three different forms of combining three lines into one.

1. Prove: The three angles of an equilateral triangle are equal, and each angle is equal to 60°.

2. As shown in the figure, in triangle ABD, C is a point on BD, and AC is perpendicular to BD, AC=BC=CD.

(1) Verify: △ABD is an isosceles triangle

(2) Find the degree of ∠ABD

Keywords: Proof courseware, can you prove them? courseware, Beijing Normal University edition ninth grade mathematics volume 1 PPT courseware, ninth grade mathematics slide courseware download, proof PPT courseware download, can you prove them PPT courseware download, .ppt format

For more information about the PPT courseware "Prove Can You Prove Them", please click the Prove ppt Can You Prove Them ppt tag.

"Can you prove them" Proof PPT courseware 4:

"Can you prove them" Proof PPT courseware 4 Properties of an isosceles triangle: Theorem: The two base angles of an isosceles triangle are equal Corollary: The bisector of the vertex angle of an isosceles triangle, the midline on the base, and the height on the base The lines coincide with each other (three lines merge into one) Conclusion 1: Equilateral triangle..

"Can you prove them" Proof PPT courseware 2:

"Can You Prove Them" Proof PPT Courseware 2 Definition A triangle with two equal sides is called an isosceles triangle; the property theorem The two base angles of an isosceles triangle are equal. Abbreviation: equilateral opposite angles. Corollary of the property theorem Isosceles triangle top The bisector of an angle, the median of the base...

"Can you prove them" Proof PPT courseware:

"Can You Prove Them" Proof PPT courseware 1. Review and consolidate the relevant content of proof (1) last semester; 2. Understand the contents of several axioms that are the basis of proof, and master the basic steps and writing format of proof. 3. Experience the process of exploration-discovery-conjecture-prove...

File Info

Update Time: 2024-09-30

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

Preview